The molality of a solution is defined as the number of moles of solute per kilogram of solvent. In this case, we are given a 1M solution of NaNO3 with a density of 1.25 g/mL and a molar mass of NaNO3 as 85 g/mol. We need to calculate the molality of this solution.

To find the molality, we first need to determine the number of moles of NaNO3 in the solution.

Step 1: Calculate the mass of NaNO3 in the solution
To find the mass of NaNO3, we can use the following formula:

Mass = Volume × Density

Given that the density of the solution is 1.25 g/mL, we can calculate the mass of the solution as follows:

Mass = 1L × 1.25 g/mL = 1250 g

Step 2: Calculate the number of moles of NaNO3
The number of moles of NaNO3 can be calculated using the formula:

Moles = Mass / Molar mass

Using the given molar mass of NaNO3 as 85 g/mol, we can calculate the number of moles as follows:

Moles = 1250 g / 85 g/mol = 14.71 mol

Step 3: Calculate the molality
Finally, we can calculate the molality using the formula:

Molality = Moles of solute / Mass of solvent (in kg)

Here, the mass of the solvent is equal to the mass of the solution minus the mass of the solute (NaNO3).

Mass of solvent = Mass of solution - Mass of solute
= 1250 g - 14.71 mol × 85 g/mol
= 1250 g - 1250 g
= 0 g

Since the mass of the solvent is zero, the molality of the solution is undefined.

Conclusion
The molality of the 1M NaNO3 solution with a density of 1.25 g/mL and a molar mass of 85 g/mol is undefined because the mass of the solvent is zero.